Evolution of CFD numerical methods and physical models towards a full discrete approach by Caltagirone, Jean-Paul

“…In recent decades, the emergence of methodologies based on differential geometry or exterior calculus has changed the point of view by starting with the creation of entangled polygonal and polyhedral structures where the variables are located. …”
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A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation by Muhammad Abid, Madiha Bibi, Nasir Yasin, Muhammad Shahid

“…Accurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson time stepping to solve the heat diffusion equation and analyze method performance.The Poisson equation is discretized using second-order central finite differences and solved with the conjugate gradient approach to determine the steady state solution. …”
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The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact by Zhi-Long He, Lin-Fei Nie

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Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model by Huidong Cheng, Fang Wang, Tongqian Zhang

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A Pest Management Model with Stage Structure and Impulsive State Feedback Control by Guoping Pang, Zhiqing Liang, Weijian Xu, Lijie Li, Gang Fu

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A Multiscale Model for Virus Capsid Dynamics by Changjun Chen, Rishu Saxena, Guo-Wei Wei

“…In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. …”
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Augmented Superfield Approach to Nilpotent Symmetries of the Modified Version of 2D Proca Theory by A. Shukla, S. Krishna, R. P. Malik

“…For the sake of completeness, we also mention, very briefly, a unique bosonic symmetry, the ghost-scale symmetry, and discrete symmetries of the theory and show that the algebra of conserved charges provides a physical realization of the Hodge algebra (satisfied by the de Rham cohomological operators of differential geometry).…”
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Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section by Zhongmin Wang, Rongrong Li

“…Combining with discretization equations for the differential equation and boundary conditions, an eigen-equation of the system including some dimensionless parameters is formulated in implicit algebraic form, so it is easy to simulate the dynamical behaviors of rotating tapered beams. …”
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Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar by Bole Ma, Yongsheng Ren

“…The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. …”
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